Updating and Optimizing Error PDFs in the Hessian Approach

TL;DR

This paper introduces the ePump software for efficiently updating and optimizing parton distribution function error sets using the Hessian method, enabling rapid impact predictions of new data on PDFs and observables.

Contribution

The paper presents a novel software tool, ePump, that streamlines updating and optimizing PDF error sets within the Hessian framework, reducing computational effort compared to full global analyses.

Findings

ePump effectively updates PDFs with new data impacts.

The method accurately predicts changes in PDF uncertainties.

Applications to LHC phenomenology demonstrate practical utility.

Abstract

We discuss how to apply the Hessian method (i) to predict the impact of a new data set (or sets) on the parton distribution functions (PDFs) and their errors, by producing an updated best-fit PDF and error PDF sets, such as the CTEQ-TEA PDFs; (ii) to predict directly the effect of a new data set on the PDF errors of any other set of observables, without the need to recalculate using the new error PDFs; and (iii) to transform the original set into a reduced set of error PDFs which is optimized for a specific set of observables to reproduce the PDF-induced uncertainties to any specified precision. We present a software package, {\tt ePump} (error PDF Updating Method Package), that can be used to update or optimize a set of PDFs, including the best-fit PDF set and Hessian eigenvector pairs of PDF sets (i.e., error PDFs), and to update any other set of observables. We demonstrate the potential of the program by presenting selected phenomenological applications relevant to the Large Hadron Collider. Special care is given to discuss the assumptions made and the limitations of this theoretical framework compared to a treatment by the full global analysis program.